As you may know, although the official Nintendo WFC have been shut down for 5 years now, fans have gotten their own WFC servers up and running. This thread is for Gens 4 and 5.
Instructions:
https://www.reddit.com/r/pokemon/comments/a1xc5q/complete_guide_for_setting_up_wifi_in_gens_4_and_5/https://drive.google.com/file/d/1mwXB1qjAJm_mJhTVfQvhDr39AoYLtE3H/viewAnd yes, just about EVERY Wi-Fi feature for Gens 4 and 5 work. Even Mystery Gifts! In fact, all Mystery Events (items, pokemon, etc, even the ones that were never released, like the Azure Flute) are available. However, when you have the game search for a mystery gift through Wi-Fi, you can't choose what gift to get; the game randomly gives you an event from the list of event items/pokemon each time you search (and sometimes it just doesn't, giving you an "error"). If you didn't get the gift you want or didn't get one at all, just try again until you do.